Like staring into a Da Vinci painting ... Fans preview the film Avatar at Comic-Con 2009 in California. Photograph: John Shearer/Getty

James Cameron's new 3D film Avatar has a lot to teach us about the Renaissance. Reviews based on early clips from this film, a sci-fi adventure due out in December, speak in awe of the new 3D technology developed by Cameron. There is a collective intake of breath at the unprecedented depth of field it creates and the convincing sense of looking not at a flat screen, but into a world of solid forms in real space.

Naturally enough, the analogy most reports reach for is the craze for 3D films in the 1950s, when spectacle-wearing audiences were wowed by films such as House of Wax. But it also evokes a much older cultural revolution.

In the 15th century, artists discovered how to paint bodies and landscapes as if they had depth and solidity. Painting triumphed over the flat surface to create the illusion of a real scene glimpsed through the square enclosure of the wooden panel or canvas, as if you were watching a play on a stage.

The effect was just as dazzling, just as unexpected as 3D cinema – and it has lasted a lot longer than the gimmicks of 1950s science fiction. Visitors to the National Gallery stand fascinated by the illusion of a real room, with real shadows, depth – even real air – in Jan van Eyck's painting the Arnolfini portrait.

Depth in painting evolved haphazardly in northern Europe, discovered through trial and error by painters like Van Eyck. In Florence, meanwhile, it was consciously theorised and scientifically analysed, resulting in what has been called a science of art.

I think we're right to be excited by three-dimensional technology; the thrill of seeing deep space on screen is not unlike the thrill of peering into one of Leonardo da Vinci's paintings. And while you can buy tickets for Avatar later this year – go and see the Arnolfini portrait for now.

This morning saw the first ever screening of 15 minutes of footage from James Cameron's film Avatar. The 3D landscapes are spectacular, writes Ben Child - shame the alien romance has so much less depth